Physics 41 HW Set 1 Chapter 15

P 5 The position of a particle is given by the expression x = (4.00 m) cos(3.00 t + ), where
x is in meters and t is in seconds. Determine (a) the frequency and period of the motion, (b) the
amplitude of the motion, (c) the phase constant, and (d) the position of the particle at t = 0.250
s.
x
4.00 m cos 3.00 t
Compare this with x A cos t
to find
(a) 2 f
3.00
or
f 1.50 H z
1
T
f
0.667 s
(b)
(c)
A
4.00 m
rad
(d) xt
0.250 s 4.00 m cos 1.75 2.83 m
P8. A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations. Find (a) the
period of its motion, (b) the frequency in hertz, and (c) the angular frequency in radians per
second.
(a)
12.0 s
T
5
2.40 s
(b)
f
1 1
T
2.40
0.417 Hz
(c) f
2 2 0.417 2.62 rad s
P18. A 200-g block is attached to a horizontal spring and executes simple harmonic motion
with a period of 0.250 s. If the total energy of the system is 2.00 J, find (a) the force constant of
the spring and (b) the amplitude of the motion.
2
2
m 200 g , T 0.250 s, E 2.00 J;
25.1 rad s
T 0.250
2
(a) k m
2
0.200 kg 25.1 rad s 126 N m
(b)
kA
2 2E
E A 2 2.00
2 k 126
0.178 m